We consider a class of plane orthotropic deformations of the form ex = σx + a12σy, γxy = 2(p − a12)Txy, ey = a12σx + σy, where σx, Txy, σy and$$ {\upvarepsilon}_x\frac{\upgamma_{xy}}{2},{\upvarepsilon}_Y $$ are components of the stress tensor and the deformation tensor, respectively, real parameters p and a12 satisfy the inequalities: -1 < p < 1, -1 < a12 < p. A class of solutions of the Lame equilibrium system for displacements is built in the form of linear combinations of components of “analytic” functions which take values in commutative and associative two-dimensional algebras with unity over the field of complex numbers.